Related papers: On periodic homeomorphisms of spheres
This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.
The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of…
We study random spherical harmonics at shrinking scales. We compare the mass assigned to a small spherical cap with its area, and find the smallest possible scale at which, with high probability, the discrepancy between them is small…
This article addresses the regularity issue for stationary or minimizing fractional harmonic maps into spheres of order $s\in(0,1)$ in arbitrary dimensions. It is shown that such fractional harmonic maps are $C^\infty$ away from a small…
We measure elastomechanical spectra for a family of thin shells. We show that these spectra can be described by a "semiclassical" trace formula comprising periodic orbits on geodesics, with the periods of these orbits consistent with those…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
The spaces of flattenings of a simplicial sphere played a key role in the study of existence and uniqueness of differentiable structures on a simplicial sphere. In this paper, we will establish that the spaces of flattenings of some…
We prove that for a generic family of circle diffeomorphisms every parameter value that corresponds to an irrational rotation number is approximated by parameter values for which the diffeomorphisms have arbitrarily large finite numbers of…
This note presents a method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will…
We study the set of periods of the Morse--Smale diffeomorphisms on the $n$-dimensional sphere $\mathbb{S}^n$, on products of two spheres of arbitrary dimension $\mathbb{S}^m \times \mathbb{S}^n$ with $m \neq n$, on the $n$-dimensional…
This paper concerns on linked periodic orbits of orientation-preserving homeomorphisms of the $2$-disc in the sense of Gambaudo. We interpret the linking of periodic orbits by using their induced braids. Then based on the forcing relation…
One of the main problems of the theory of dynamical systems is the determination of the existence of periodic orbits of a self-map and more generally, the structure of the set of periods. Define the minimum period of a class os self-maps of…
The self-gravitating, spherically symmetric thin shells built of orbiting particles are sstudied. Two new features are found. One is the minimal possible value for an angular momentum of particles, above which elleptic orbits become…
The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…
The aim of this work is to describe the set of fixed point free homeomorphisms of the plane under certain expansive conditions.
We characterize the limit periodic sets of families of polynomial planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere with…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…
It is known that any periodic map of order $n$ on a closed oriented surface of genus $g$ can be equivariantly embedded into $S^m$ for some $m$. In the orientable and smooth category, we determine the smallest possible $m$ when $n\geq 3g$.…
The goal of this paper is to give a detailed and complete proof of M. Gromov's waist of the sphere theorem.